In informal speech, factions usually refers to the higher powers: the Kami and the Karavan. Most often when people use the term factions, this is what they refer to.

This use matches general online games lingo because most games make players choose between two opposing sides referred to as the two factions.

In Ryzom specifically, until recently Faction points could only be earned with the Kami and the Karavan, and Faction PvP was always Kami versus Karavan. This is no longer the case (see below) but the terminology has stuck.

Though it is often used so informally, no official source refers to the Kami and Karavan as the factions; they are referred to as the higher powers, the religions or the cults.

From the very beginning, the players who didn't align with any faction and thus remained neutral have often been referred to as the third faction (in the case of the higher powers) or the fifth faction (in the case of the civilizations). It's a matter of opinion whether neutrality is actually a faction or rather the lack of faction.

This issue was only complicated further when different kinds of neutral were implemented: Hominists who are friendly with all nations, Marauders who are hostile to all nations, Theists who are friendly with both higher powers and Antitheists who are hostile to both higher powers. All those groups also get their own Faction PvP icon.

And ofcourse, there are still the remaining neutrals who don't fall into any of those groups. So all in all there are now 6 different neutral factions.